TSTP Solution File: GRP592-1 by Toma---0.4
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%------------------------------------------------------------------------------
% File : Toma---0.4
% Problem : GRP592-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : toma --casc %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 01:15:27 EDT 2023
% Result : Unsatisfiable 37.23s 37.49s
% Output : CNFRefutation 37.23s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRP592-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.07/0.13 % Command : toma --casc %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 02:14:20 EDT 2023
% 0.13/0.34 % CPUTime :
% 37.23/37.49 % SZS status Unsatisfiable
% 37.23/37.49 % SZS output start Proof
% 37.23/37.49 original problem:
% 37.23/37.49 axioms:
% 37.23/37.49 double_divide(inverse(double_divide(double_divide(A, B), inverse(double_divide(A, inverse(C))))), B) = C
% 37.23/37.49 multiply(A, B) = inverse(double_divide(B, A))
% 37.23/37.49 goal:
% 37.23/37.49 multiply(a(), b()) != multiply(b(), a())
% 37.23/37.49 To show the unsatisfiability of the original goal,
% 37.23/37.49 it suffices to show that multiply(a(), b()) = multiply(b(), a()) (skolemized goal) is valid under the axioms.
% 37.23/37.49 Here is an equational proof:
% 37.23/37.49 0: double_divide(inverse(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(X2))))), X1) = X2.
% 37.23/37.49 Proof: Axiom.
% 37.23/37.49
% 37.23/37.49 1: multiply(X0, X1) = inverse(double_divide(X1, X0)).
% 37.23/37.49 Proof: Axiom.
% 37.23/37.49
% 37.23/37.49 2: X2 = double_divide(inverse(double_divide(double_divide(inverse(double_divide(double_divide(X3, inverse(X2)), inverse(double_divide(X3, inverse(X5))))), X1), inverse(X5))), X1).
% 37.23/37.49 Proof: A critical pair between equations 0 and 0.
% 37.23/37.49
% 37.23/37.49 3: X2 = double_divide(inverse(double_divide(X5, inverse(double_divide(inverse(double_divide(double_divide(X3, X4), inverse(double_divide(X3, inverse(X5))))), inverse(X2))))), X4).
% 37.23/37.49 Proof: A critical pair between equations 0 and 0.
% 37.23/37.49
% 37.23/37.49 4: X2 = double_divide(inverse(double_divide(X8, inverse(X8))), inverse(X2)).
% 37.23/37.49 Proof: A critical pair between equations 3 and 0.
% 37.23/37.49
% 37.23/37.49 6: X2 = double_divide(inverse(double_divide(X5, inverse(double_divide(inverse(double_divide(X8, inverse(double_divide(inverse(double_divide(double_divide(X6, X7), inverse(double_divide(X6, inverse(X8))))), inverse(X5))))), inverse(X2))))), X7).
% 37.23/37.49 Proof: A critical pair between equations 3 and 0.
% 37.23/37.49
% 37.23/37.49 8: X2 = double_divide(inverse(double_divide(double_divide(inverse(double_divide(X8, inverse(double_divide(inverse(double_divide(double_divide(X6, inverse(X2)), inverse(double_divide(X6, inverse(X8))))), inverse(X5))))), X1), inverse(X5))), X1).
% 37.23/37.49 Proof: A critical pair between equations 2 and 0.
% 37.23/37.49
% 37.23/37.49 16: X2 = double_divide(inverse(double_divide(X10, inverse(X2))), inverse(X10)).
% 37.23/37.49 Proof: A critical pair between equations 2 and 4.
% 37.23/37.49
% 37.23/37.49 17: X2 = double_divide(inverse(inverse(double_divide(X9, inverse(X9)))), inverse(X2)).
% 37.23/37.49 Proof: A critical pair between equations 4 and 4.
% 37.23/37.49
% 37.23/37.49 19: X2 = double_divide(inverse(double_divide(double_divide(inverse(double_divide(X2, inverse(X10))), X1), inverse(X10))), X1).
% 37.23/37.49 Proof: A critical pair between equations 8 and 4.
% 37.23/37.49
% 37.23/37.49 21: X2 = double_divide(inverse(double_divide(X10, inverse(double_divide(inverse(double_divide(X8, inverse(X10))), inverse(X2))))), inverse(X8)).
% 37.23/37.49 Proof: A critical pair between equations 6 and 4.
% 37.23/37.49
% 37.23/37.49 28: X11 = double_divide(inverse(X12), inverse(inverse(double_divide(X11, inverse(X12))))).
% 37.23/37.49 Proof: A critical pair between equations 16 and 16.
% 37.23/37.49
% 37.23/37.49 29: X12 = double_divide(inverse(X12), inverse(inverse(double_divide(X11, inverse(X11))))).
% 37.23/37.49 Proof: A critical pair between equations 16 and 4.
% 37.23/37.49
% 37.23/37.49 30: X2 = double_divide(inverse(inverse(inverse(double_divide(X10, inverse(X10))))), inverse(X2)).
% 37.23/37.49 Proof: A critical pair between equations 17 and 4.
% 37.23/37.49
% 37.23/37.49 31: X12 = double_divide(inverse(X12), inverse(inverse(inverse(double_divide(X11, inverse(X11)))))).
% 37.23/37.49 Proof: A critical pair between equations 16 and 17.
% 37.23/37.49
% 37.23/37.49 32: X2 = double_divide(inverse(inverse(inverse(inverse(double_divide(X10, inverse(X10)))))), inverse(X2)).
% 37.23/37.49 Proof: A critical pair between equations 17 and 17.
% 37.23/37.49
% 37.23/37.49 35: X2 = double_divide(inverse(double_divide(double_divide(X11, inverse(X13)), inverse(X13))), inverse(double_divide(X11, inverse(X2)))).
% 37.23/37.49 Proof: A critical pair between equations 21 and 0.
% 37.23/37.49
% 37.23/37.49 36: inverse(double_divide(X11, inverse(X12))) = double_divide(inverse(double_divide(double_divide(inverse(X12), X1), inverse(X11))), X1).
% 37.23/37.49 Proof: A critical pair between equations 19 and 16.
% 37.23/37.49
% 37.23/37.49 42: multiply(inverse(X12), X11) = double_divide(multiply(inverse(X11), double_divide(inverse(X12), X1)), X1).
% 37.23/37.49 Proof: Rewrite equation 36,
% 37.23/37.49 lhs with equations [1]
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 43: X2 = double_divide(multiply(inverse(X13), double_divide(X11, inverse(X13))), multiply(inverse(X2), X11)).
% 37.23/37.49 Proof: Rewrite equation 35,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1,1].
% 37.23/37.49
% 37.23/37.49 45: X2 = double_divide(inverse(inverse(inverse(multiply(inverse(X10), X10)))), inverse(X2)).
% 37.23/37.49 Proof: Rewrite equation 32,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 46: X12 = double_divide(inverse(X12), inverse(inverse(multiply(inverse(X11), X11)))).
% 37.23/37.49 Proof: Rewrite equation 31,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 47: X2 = double_divide(inverse(inverse(multiply(inverse(X10), X10))), inverse(X2)).
% 37.23/37.49 Proof: Rewrite equation 30,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 48: X12 = double_divide(inverse(X12), inverse(multiply(inverse(X11), X11))).
% 37.23/37.49 Proof: Rewrite equation 29,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 49: X11 = double_divide(inverse(X12), inverse(multiply(inverse(X12), X11))).
% 37.23/37.49 Proof: Rewrite equation 28,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 61: X2 = double_divide(multiply(inverse(X8), X8), inverse(X2)).
% 37.23/37.49 Proof: Rewrite equation 4,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 62: double_divide(multiply(multiply(inverse(X2), X0), double_divide(X0, X1)), X1) = X2.
% 37.23/37.49 Proof: Rewrite equation 0,
% 37.23/37.49 lhs with equations [1,1]
% 37.23/37.49 rhs with equations [].
% 37.23/37.49
% 37.23/37.49 66: X2 = double_divide(inverse(multiply(inverse(X9), X9)), inverse(X2)).
% 37.23/37.49 Proof: Rewrite equation 17,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 78: multiply(inverse(X12), double_divide(inverse(X12), inverse(X14))) = X14.
% 37.23/37.49 Proof: A critical pair between equations 42 and 61.
% 37.23/37.49
% 37.23/37.49 81: multiply(inverse(inverse(multiply(inverse(X10), X10))), X14) = X14.
% 37.23/37.49 Proof: A critical pair between equations 47 and 49.
% 37.23/37.49
% 37.23/37.49 85: inverse(multiply(inverse(X14), X14)) = multiply(inverse(X9), X9).
% 37.23/37.49 Proof: A critical pair between equations 66 and 46.
% 37.23/37.49
% 37.23/37.49 86: multiply(inverse(X14), X14) = inverse(inverse(multiply(inverse(X10), X10))).
% 37.23/37.49 Proof: A critical pair between equations 45 and 48.
% 37.23/37.49
% 37.23/37.49 91: inverse(double_divide(X14, inverse(inverse(inverse(double_divide(X10, inverse(X10))))))) = X14.
% 37.23/37.49 Proof: Rewrite equation 81,
% 37.23/37.49 lhs with equations [1,1]
% 37.23/37.49 rhs with equations [].
% 37.23/37.49
% 37.23/37.49 92: inverse(double_divide(double_divide(inverse(X12), inverse(X14)), inverse(X12))) = X14.
% 37.23/37.49 Proof: Rewrite equation 78,
% 37.23/37.49 lhs with equations [1]
% 37.23/37.49 rhs with equations [].
% 37.23/37.49
% 37.23/37.49 105: double_divide(inverse(double_divide(double_divide(X0, X1), inverse(double_divide(X0, inverse(X2))))), X1) = X2.
% 37.23/37.49 Proof: Rewrite equation 62,
% 37.23/37.49 lhs with equations [1,1]
% 37.23/37.49 rhs with equations [].
% 37.23/37.49
% 37.23/37.49 118: X11 = double_divide(inverse(X12), inverse(inverse(double_divide(X11, inverse(X12))))).
% 37.23/37.49 Proof: Rewrite equation 49,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 124: X2 = double_divide(inverse(double_divide(double_divide(X11, inverse(X13)), inverse(X13))), inverse(double_divide(X11, inverse(X2)))).
% 37.23/37.49 Proof: Rewrite equation 43,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1,1].
% 37.23/37.49
% 37.23/37.49 127: inverse(double_divide(X14, inverse(X14))) = inverse(inverse(inverse(double_divide(X10, inverse(X10))))).
% 37.23/37.49 Proof: Rewrite equation 86,
% 37.23/37.49 lhs with equations [1]
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 128: inverse(inverse(double_divide(X14, inverse(X14)))) = inverse(double_divide(X9, inverse(X9))).
% 37.23/37.49 Proof: Rewrite equation 85,
% 37.23/37.49 lhs with equations [1]
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 138: X14 = inverse(double_divide(X14, inverse(double_divide(X16, inverse(X16))))).
% 37.23/37.49 Proof: A critical pair between equations 91 and 127.
% 37.23/37.49
% 37.23/37.49 143: X15 = double_divide(inverse(X15), inverse(double_divide(X16, inverse(X16)))).
% 37.23/37.49 Proof: A critical pair between equations 118 and 128.
% 37.23/37.49
% 37.23/37.49 145: X2 = double_divide(X15, inverse(double_divide(inverse(X15), inverse(X2)))).
% 37.23/37.49 Proof: A critical pair between equations 124 and 92.
% 37.23/37.49
% 37.23/37.49 148: X2 = double_divide(X15, multiply(inverse(X2), inverse(X15))).
% 37.23/37.49 Proof: Rewrite equation 145,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 149: X15 = double_divide(inverse(X15), multiply(inverse(X16), X16)).
% 37.23/37.49 Proof: Rewrite equation 143,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 152: X14 = multiply(multiply(inverse(X16), X16), X14).
% 37.23/37.49 Proof: Rewrite equation 138,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1,1].
% 37.23/37.49
% 37.23/37.49 161: X11 = double_divide(inverse(X12), inverse(multiply(inverse(X12), X11))).
% 37.23/37.49 Proof: Rewrite equation 118,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 174: double_divide(multiply(multiply(inverse(X2), X0), double_divide(X0, X1)), X1) = X2.
% 37.23/37.49 Proof: Rewrite equation 105,
% 37.23/37.49 lhs with equations [1,1]
% 37.23/37.49 rhs with equations [].
% 37.23/37.49
% 37.23/37.49 203: inverse(inverse(X17)) = X17.
% 37.23/37.49 Proof: A critical pair between equations 148 and 149.
% 37.23/37.49
% 37.23/37.49 204: X17 = double_divide(double_divide(X17, X1), X1).
% 37.23/37.49 Proof: A critical pair between equations 174 and 152.
% 37.23/37.49
% 37.23/37.49 242: X11 = double_divide(inverse(X12), double_divide(X11, inverse(X12))).
% 37.23/37.49 Proof: Rewrite equation 161,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [1,203].
% 37.23/37.49
% 37.23/37.49 277: X11 = double_divide(X18, double_divide(X11, inverse(inverse(X18)))).
% 37.23/37.49 Proof: A critical pair between equations 242 and 203.
% 37.23/37.49
% 37.23/37.49 279: X11 = double_divide(X18, double_divide(X11, X18)).
% 37.23/37.49 Proof: Rewrite equation 277,
% 37.23/37.49 lhs with equations []
% 37.23/37.49 rhs with equations [203].
% 37.23/37.49
% 37.23/37.49 308: double_divide(X19, X20) = double_divide(X20, X19).
% 37.23/37.49 Proof: A critical pair between equations 279 and 204.
% 37.23/37.49
% 37.23/37.49 325: multiply(a(), b()) = multiply(b(), a()).
% 37.23/37.49 Proof: Rewrite lhs with equations [1,308]
% 37.23/37.49 rhs with equations [1].
% 37.23/37.49
% 37.23/37.49 % SZS output end Proof
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